Venn diagram questions come in two forms: you are given a diagram and asked what it shows, or you are given information and asked which diagram fits it. Either way, the skill is the same — knowing exactly which region each phrase refers to.
Name the regions first
With two circles A and B there are four regions: only A, only B, both, and neither. With three circles there are eight. Spend five seconds labelling them before reading the options. It saves you from the most common error, which is counting the overlap twice.
- "A" or "in A" — every region inside circle A, including the overlaps.
- "Only A" — the part of A that does not touch any other circle.
- "A and B" — the overlap, which may include the centre if there is a third circle.
- "A or B" — everything inside either circle, counted once.
When the numbers are given in words
- Start with the region that belongs to the most groups (the centre).
- Subtract it from each pairwise overlap to find the "exactly two" regions.
- Subtract the overlaps from each circle total to find the "only" regions.
- Check that all regions add up to the total given.
💡 If a question says "at least two", add the exactly-two regions and the centre. If it says "exactly two", leave the centre out.
Choosing the diagram that fits
When several diagrams are offered, test each one against the statements one at a time. A single region that should be empty but is not (or the reverse) rules a diagram out. Eliminating is faster than proving one correct.